Correlations between grey-level variations in 2D projection images (TBS) and 3D microarchitecture: applications in the study of human trabecular bone microarchitecture.

X-ray imaging remains a very cost-effective technique, with many applications in both medical and material science. However, the physical process of X-ray imaging transforms (e.g. projects) the 3-dimensional (3D) microarchitecture of the object or tissue being studied into a complex 2D grey-level texture. The 3D/2D projection process continues to be a difficult mathematical problem, and neither demonstrations nor well-established correlations have positioned 2D texture analysis-based measurement as a valid indirect evaluation of 3D microarchitecture. The trabecular bone score (TBS) is a new grey-level texture measurement which utilizes experimental variograms of 2D projection images. The aim of the present study was to determine the level of correlation between the 3D characteristics of trabecular bone microarchitecture, as evaluated using muCT reconstruction, and TBS, as evaluated using 2D projection images derived directly from 3D muCT reconstruction. Analyses were performed using sets of human cadaver bone samples from different anatomical sites (lumbar spine, femoral neck, and distal radius). Significant correlations were established via standard multiple regression analysis, and via the use of a generic mathematical 3D/2D relationship. In both instances, the correlations established a significant relationship between TBS and two 3D characteristics of bone microarchitecture: bone volume fraction and mean bone thickness. In particular, it appears that TBS permits to accurately differentiate between two 3D microarchitectures that exhibit the same amount of bone, but different trabecular characteristics. These results demonstrate the existence of a robust and generic relationship, taking into consideration a simplified model of a 2D projection image. Ultimately, this may lead to using TBS measurements directly on DXA images obtained in routine clinical practice.